Existence, non-existence and blow-up behavior of minimizers for the mass-critical fractional nonlinear Schrödinger equations with periodic potentials

2019/12/18 by Dinh, Van Duong · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.08750

Abstract

We consider the minimizing problem for the energy functional with prescribed mass constraint related to the fractional nonlinear Schrödinger equation with periodic potentials. Using the concentration-compactness principle, we show a complete classification for the existence and non-existence of minimizers for the problem. In the mass-critical case, under a suitable assumption of the potential, we give a detailed description of blow-up behavior of minimizers once the mass tends to a critical value.

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• The uniqueness and concentration behavior of solutions for a nonlinear fractional Schrödinger system

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